Step |
Hyp |
Ref |
Expression |
1 |
|
peano1 |
|
2 |
|
eleq1 |
|
3 |
1 2
|
mpbiri |
|
4 |
3
|
adantr |
|
5 |
4
|
pm4.71ri |
|
6 |
5
|
opabbii |
|
7 |
|
omex |
|
8 |
7
|
a1i |
|
9 |
|
simp1 |
|
10 |
|
unab |
|
11 |
|
abrexexg |
|
12 |
11
|
3ad2ant2 |
|
13 |
|
abrexexg |
|
14 |
13
|
3ad2ant3 |
|
15 |
|
unexg |
|
16 |
12 14 15
|
syl2anc |
|
17 |
10 16
|
eqeltrrid |
|
18 |
17
|
ralrimivw |
|
19 |
|
abrexex2g |
|
20 |
9 18 19
|
syl2anc |
|
21 |
20
|
adantr |
|
22 |
8 21
|
opabex3rd |
|
23 |
|
simpr |
|
24 |
23
|
anim2i |
|
25 |
24
|
ssopab2i |
|
26 |
25
|
a1i |
|
27 |
22 26
|
ssexd |
|
28 |
6 27
|
eqeltrid |
|